In a statement to news.com.au, Ms Price said she "unequivocally" disputed the version of events and insisted her conversation was "cordial and relaxed".

"Former President Tong and I discussed the prospect of meeting officially at some time in the future. At no point did I make the sort of comments Senator Dodson is alleging," the statement read.

"I have spoken to Senator Dodson to convey that I dispute the version (of) events in his letter addressed to me. I spoke to former President Tong a short time ago and he thanked me for reaching out to him."

The letter sent by Senator Patrick Dodson to Environment Minister Melissa Price.